Magnetization reversal of interconnected kagome artificial spin ice was studied by the first-order reversal curve (FORC) technique based on the magneto-optical Kerr effect and magnetoresistance measurements. The magnetization reversal exhibits a distinct sixfold symmetry with the external field orientation. When the field is parallel to one of the nano-bar branches, the domain nucleation/propagation and annihilation processes sensitively depend on the field cycling history and the maximum field applied. When the field is nearly perpendicular to one of the branches, the FORC measurement reveals the magnetic interaction between the Dirac strings and orthogonal branches during the magnetization reversal process. Our results demonstrate that the FORC approach provides a comprehensive framework for understanding the magnetic interaction in the magnetization reversal processes of spin-frustrated systems.